Span, Danny Espinosa and Adam LaRoche had two hits apiece as Washington won the final two games of the series.
The Nationals improved to 3-7 against Atlanta. They increased their division lead over the Braves to 1 1/2 games.
Roark (7-4) went 5 1-3 innings, allowing a run and four hits.
Craig Stammen came on to end a sixth-inning Braves rally, and Rafael Soriano pitched the ninth for his 17th save. Washington relievers retired all 11 batters they faced.
Freddie Freeman had two hits for Atlanta. Evan Gattis went 0 for 3 to snap his 20-game hitting streak.
Ervin Santana (5-5) went six innings, giving up three runs and six hits. He walked one and struck out nine.
Atlanta's Chris Johnson was ejected for arguing a checked-swing call in the sixth. Teammate Justin Upton was ejected for arguing after a swinging strikeout in the ninth.
With Washington leading 3-0, the first two Braves reached against Roark in the sixth. Manager Matt Williams visited the mound but left Roark in to face Jason Heyward. Roark got Heyward on a fly to right, but Justin Upton singled home Freddie Freeman to make 3-1.
Stammen came on to pitch to Johnson, who attempted to check his swing on a 1-2 pitch. Nationals catcher Sandy Leon appealed the ball call, and first base umpire Tim Welke ruled Johnson had gone around for strike three.
Johnson immediately began yelling and gesturing at Welke and was ejected by home plate umpire Mark Carlson. Stammen retired Andrelton Simmons to end the inning.
Anthony Rendon made it 4-1 when he doubled in the eighth, went to third on a ground out and scored on Luis Avilan's wild pitch.
Washington got to Santana in the first, getting and RBI single from LaRoche that deflected off diving shortstop Simmons' glove. Ryan Zimmerman had a sacrifice fly to make it 2-0.
Atlanta threatened in the third. With one out, LaRoche misplayed Freeman's grounder down the first base line for a two-base error. But Roark got Gattis on a grounder to third, and, after Heyward walked, Justin Upton hit into a fielder's choice.
The Nationals made it 3-0 the fifth.
Sandy Leon opened with a single and Roark sacrificed him to second. Span then lined a double to left, scoring Leon. Span is 6 for his last 11 against Santana.
NOTES: Nationals C Wilson Ramos (left hamstring strain) went 1 for 3 with a homer and three RBIs in his first rehab game with Double-A Harrisburg Saturday night. He's expected to rejoin the Nationals this week. Freeman began the day as one of only three NL players to start all of their team's games, along with Starlin Castro (Cubs) and Hunter Pence (Giants). Atlanta is off Monday before opening a 3-game series Tuesday in Houston. Gio Gonzalez (3-4, 4.85) opposes Matt Garza (4-4, 4.02) Monday when Washington opens a 3-game series at Milwaukee.